Bell gyro and improved means for operating same

ABSTRACT

A bell-like high-Q member for detecting motion of a platform about an axis and having a lip capable of sustaining therein a vibration pattern having alternately and equi-angularly spaced nodal and anti-nodal regions of radial vibration when the lip is exercised radially. Pickoff electrodes located at regions nodal in the absence of rotation about the axis detect radial vibrations developed thereat due to the effects on the vibrations pattern of the rotation about the axis. Forcer electrodes located at other regions nodal in the absence of rotation are connected in circuit with the pickoff electrodes to null such radial vibrations.

[is] 3,656,354 [451 Apr. 18, 1972 [s41 BELL GYRO AND IMPROVED MEANS FOR OPERATING SAME [72] lnventor: David D. Lynch, Greendale, Wis.

[73] Assignee: General Motors Corporation, Detroit,

Mich.

[22] Filed: Oct. 6, 1969 [21] Appl.No.: 864,019

[52] U.S. Cl ..73/505 2,455,939 12/1948 Meredith..... 3,307,409 3/1967 Newton Illlllllla,

3,408,872 11/1968 Simmonsetal ..73/505 Primary Examiner-James J. Gill Attorney-E. W. Christen, A. F. Duke and C. R. Meland [57] ABSTRACT A bell-like high-Q member for detecting motion of a platform about an axis and having a lip capable of sustaining therein a vibration pattern having alternately and equi-angularly spaced nodal and anti-nodal regions of radial vibration when the lip is exercised radially. Pickoff electrodes located at regions nodal in the absence of rotation about the axis detect radial vibrations developed thereat due to the effects on the vibrations pattern of the rotation about the axis. Forcer electrodes located at other regions nodal in the absence of rotation are connected in circuit with the pickolf electrodes to null such radial vibrations.

10 Claims, 5 Drawing Figures PATENTEDAPR 18 m2 3. 656, 354

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PATENTEDAPR 18 I972 SHEET 3 [IF 4 HEOKUE .rDOa (mm ATTORNEY BELL GYRO AND IMPROVED MEANS FOR OPERATING SAME This invention relates to an improved device for detecting motion about an axis therethrough by imparting, sensing and maintaining radial vibrations in a high-Q member capable of sustaining therein a vibration pattern having nodal and anti nodal regions spaced alternately and equi-angularly thereabout. It is particularly directed to a method and apparatus applying the general method and means described and claimed in US. patent application Ser. No. 843,109, entitled Device for Detecting Rotation about an Axis and Method of Sensing Same," filed by Alfred G. Emslie on July 18, 1969, and also to improved devices for applying this method and means described and claimed in U.S. patent applications Ser. Nos. 863,861 and 863,857, entitled Bell Gyro and Method of Making Same and Improved Bell Gyro and Method of Making Same, both the latter applications filed by Richard E. Denis on the same date as the present application. All three such applications are assigned to the same assignee as the present invention and are incorporated herein by reference. Such devices are so arranged and operated in the present invention to afford improved sensitivity, linearity of output, and range of operation with input rotations of varying magnitudes and frequencies.

A characteristic inherent in bell-like rotation detectors of the type described and claimed in the above Emslie and Denis patent applications is that the vibrations produced at the nodal regions due to input rotation and other factors tend to add and subtract from the vibrations of the exercising .pattern. This in effect tends to rotate the exercising pattern in azimuth about the input axis. This rotation is undesirable. Since the forcer and sensor comprising the self-oscillating loop employed in such devices maintains the anti-nodal regions of the exercising pattern at constant amplitude in the absence of rotation, one result of such pattern rotation is to increase the amplitude of the rotated anti-nodal region and introduce further vibration in the pickup regions due purely to the rotation of the vibration pattern rather than the input rotation (although these effects are not wholly unrelated). This creates noise at the pickoff regionsand tends to make the output detected in the presence of input rotation to be less linear with input as the input rate increases.

Another inherent characteristic of bell-like rotation detectors of the aforementioned type is that a slight difference in vibration frequencies inevitably exists along the forcing and pickup axes. Such differences, called non-degeneracy of frequencies, introduces frequency side-band effects which tend to alter the amplitude detected at the pickup regions. Such non-degeneracymoreover could also vary the phase of the pickup vibrations relative to forcing vibrations and even the frequency of both the forcing and pickup vibrations. This effect is moreover, accentuated as both the magnitude or frequency of input rotation increases. Therefore, the range of input rates over which the pickup output is adequately linear with input is reduced, and the band of input frequencies over which the instrumentis linearly sensitive is lessened.

Yet another fundamental inherent characteristic of bell-like rotation detection is that vibrations at the anti-nodal regions are independent or orthogonal to the effects of those vibrations produced at nodal regions, and vice versa, but only to the first order. However, due to effects such as vibration-pattern rotation and frequency non-degeneracy, such vibrations are increasingly interdependent in the second order,'especially as the magnitude and frequency of the input rate increases.

Employing this inherent first-order orthogonality characteristic, the present invention in its broadest aspect substantially avoids these errors and limitations by nulling vibrations detected at a nodal region and measuring the voltage or other energy indicative value required for such nulling. It has been found that the energy so measured is linearly sensitive over a wide band of input rates and frequencies. Moreover, the shifting of the phaseof pickup and forcing vibrations with varying input rates is avoided, and the overall signal to noise ratio of the instrument is markedly enhanced.

In its preferred form and most narrow aspect, the present invention includes a high-Q bell-like member supported on the platform by a post .and depending therefrom in telescopic rela tion. The bell-like member has sides flaring arcuately outward and downwards from its axis and the post axis, terminating adjacent the platform in an annular lip capable of sustaining therein a vibration pattern having nodal and anti-nodal regions spaced alternately and equi-angularly thereabout. Telescoped within the bell-like member and supported therein by the platform and post is a forcer and sensor assembly including eight electrodes that coact with the lip of the bell-like member equiangularly thereabout. Acting in pairs, some of these electrodes impart, sense, and maintain radial vibrations of the lip at the anti-nodal regions. Other pairs of electrodes detect radial vibrations at regions nodal in the absence of rotation and then null such vibrations. More particularly, a first pair of electrodes serve as forcers or exercisers that impart radial vibrations to the lip to establish the vibration pattern therein having four nodal regions and four anti-nodal regions spaced alternately and equi-angularly about the periphery of the lip. A second pair of electrodes sense radial vibrations at two of the anti-nodal regions and are electrically connected in a feedback circuit with the first pair to generate substantially constant-amplitude natural-frequency radial vibrations at the four anti-nodal regions. A third pair of electrodes sense radial vibrations at one set of nodal regions thereby detecting the rotation or input rate of the platform about the axis. A fourth pair of electrodes at a second set of nodal regions are connected in feedback circuit, the third pair of electrodes to null the vibrations detected by the third pair.

It is therefore a general object of the present invention to provide an apparatus to measure rotation about an axis in which a high-Q member having a lip that undergoes radial vibrations in a vibration pattern having nodal and anti-nodal regions spaced alternately and equi-angularly about the axis, wherein vibrations produced at nodal regions when there is rotation are nulled so as to overcome the aforementioned problems.

It is a further object to provide a device of the foregoing type wherein vibrations produced at nodal regions are nulled along radial axes that may be disposed from the forcing axes by less than 1 It is another object to provide a device of the foregoing type where the vibrations at the nodal regionsare nulled in such fashion that the amplitude or frequency of the vibrations at the anti-nodal regions are the same in the presence of rotation as otherwise.

It is a further and more specific object to provide a high-Q member of the foregoing type operated so that the phase of the vibrations produced in the nodal regions have a constant difference from the phase of the vibrations imparted at the anti-nodal regions over input rates varying in substantial magnitudc and frequency.

Thepresent invention further has for its objects the attainment of a process and apparatus having features of construction, combination, and arrangement providing high sensitivity, linear, accurate, and otherwise effective measurement of rotation about an axis, all at low cost and with a high degree of reliability.

The novel features which I believe to be characteristic of the present invention are set forth in the annexed claims. The invention itself, together with further objects and advantages thereof, is set forth in the following description taken in connection with the accompanying drawings, wherein:

FIG. 1 is a perspective view, partially broken away, of a belllike member disposed adjacent electrodes'spaced equiangularly about the polar axis of the bell, all as used in the preferred form of the present invention.

FIG. la is a diagrammatic top-plan view of the vibrating lip portion and circuit of the apparatus of FIG. 1, with the lip shown in the neutral and in two extreme positions, shown exaggerated to indicate the action more clearly.

FIG. 2 is a block diagram of an overall system in accordance with the present invention;

FIG. 3 is a schematic representation, partially in block form, of circuit means for operating the bell; and

FIG. 4 is a chart of waveforms associated with the operation of the apparatus of FIGS. 3 and 4.

DETAILED DESCRIPTION-FIG. 1

As may be seen with reference to FIG. 1 and described more fully in the above-mentioned Denis application, bell B is comprised of arcuate sides 10 symmetrical about polar or input axis Z-Z. Sides 10 flare from central hub area 16 having upper surface 18, lower surface 20, and a coaxial bore 22 therethrough. Sides 10 are also contiguous with and terminate at cylindrical lip 14. Bell B is supported in an inverted position from central area 16 on post 24 upstanding from platform 12, and bell B and support post 24 are enclosed on platform 12 by cylindrical housing 90, as shown.

In addition to post 24, platform 12 is comprised of a concentric electrode assembly 40 having eight equi-angularly spaced electrodes 42, 44, 46, 48, 50, 52, 54, and 56. As to be described more fully below with reference to FIG. 2, electrodes 42, 48, 50, and 56 are for exercising or forcing associated regions of lip 14 radially by applying varying attractive potentials thereto; and electrodes 44, 46, 52, and 54 are for detecting or sensing radial motion of lip regions by measuring varying potentials thereat. Further elements of the electrode assembly 40 include a grounded shield comprised of hub 58 and spokes 60, a conductive and electrically-isolated guard comprised of tops 62, cylindrical web portions 64, arms 66, and base tabs 68, and connectors 78 comprised of a probe 74 and isolated guard 76.

Being grounded to platform 12 at surface 63, the shield defines peripheral openings or spaces in platform 12 to receive electrodes and isolates the sensor electrodes of low potential from adjacent forcer electrodes at a high potential. The guard elements are electrically-isolated and physicallyseparated by potting compound 70 from the platform, shield, and electrodes as shown and are maintained electrically at substantially the same potential as the sensor electrodes to enhance their sensitivity by providing a constant capacitance cage thereabout.

The platform, electrodes, shield, and guard and especially bell B are made from a high-Q or low-loss material. By high-Q, I refer to the ratio of the energy stored in the oscillating system to the energy dissipated in one cycle. Materials that exhibit favorable Qs, elastic limits, and modulus of elasticity, and yet are readily machinable, include aluminum alloys, such as 2024-T4. This alloy has a composition generally of 93.4 percent aluminum, 4.5 percent copper, 1.5 percent magnesium, and 0.6 percent manganese. Also, silicon-aluminum bronze or Everdur alloys, having 96 percent copper, 3 percent silicon, and 1 percent manganese or 91 percent copper, 7 percent aluminum and 2 percent silicon have favorable properties.

Thus, bell B shown in FIG. 1, is preferably constructed from 2024-T4 aluminum having a modulus of elasticity E of 10.6Xl psi and a Q of 3,000 in air, 3,100 in helium and up to 12,000 in torr vacuum. Sides 10 and contiguous cylindrical lip section 14 both have a mean radius of 1 inch and vary in thickness in the arcuate region from maximum h in the center region 16 to some finite thickness h in accordance with the formula h h ,(l cos 0) /4, where 6 is the spherical angle subtended from the polar axis Z--Z through center 16. This thicknesscontour is believed to provide surfaces of uniform maximum strain when flexed. The lip 14 is of constant thickness h,,/4, here approximately 0.050 inches, and has an axial length of approximately 0.25 inches along axis Z-Z. This length is believed to increase the momentum of the sides 10 to afford increased deflection thereof when acted upon by the Coriolis forces mentioned below.

Electrode assembly 40 is potted with a suitable potting adhesive 70, for example, that known as P38 obtainable from Bacon Industries of Watertown, Massachusetts. This adhesive is an epoxy resin-base compound chosen because of the stability of its composition and dimensions with time and temperature and its high dielectric strength. Moreover, such potting compound also has high adhesion, low tendency to crack, low coefficient of linear thermal expansion, low creep, and high tensile strength.

Platform 12 is completed with the insertion of feedthrough connectors 78 and printed circuit board 85. Feedthrough connectors 78 are microdot" connectors CD-OS l-007 available from Microdot Incorporated, South Pasadena, California, and are threaded into holes 75 previously tapped into potted holes 72. As shown in FIG. 1, such connectors are comprised of a bronze or copper tipped pressure-contact probe 74 electrically insulated from an enveloping guard 76 comprised of a threaded portion 76a, a sleeve portion 76b, and a flange portion 760. Threaded guard portion 76a is inserted to communicate with and terminate at guard base 68 in holes 75 therethrough.

Signals developed on the contact probe 74 are brought out thereby to printed circuit board inserted in cavity 87 counterbored at the bottom of platform 12 as shown. Board 85 carries suitable contact pads for electrical connection with the probe 74 and the guard 76 of feedthrough connector 78 and carries suitable circuit paths and elements for interconnecting the electrodes and operating the device, as to be more fully described below.

In the embodiment shown, bell B is then secured to platform 12 by means of a nut 34 and washer 36 acting on threaded area 32 of rod 30 to urge bell upper hub surface 18 and in turn lower hub surface 20 towards hub surface 26 of the post 24. Radial location of bell B is effected by the cooperation of the axial surface of bell bore 22 and post stem 28 thereby providing a gap of nominally 0.005 inches between the inside surfaces of lip 14 and surface 80.

In order to enhance the overall sensitivity of the device, a close correspondence of natural frequencies, such correspondence also known as degeneracy, is desired among all nodal and anti-nodal directions radial to polar axes Z-Z. While sides 10 of bell B are readily machinable to provide natural frequencies that are reasonably identical or degenerate along all axes perpendicular to polar axis Z-Z, the azimuth position of the bell may be adjusted about stem 28 before the tightening of nut 34 so as to align the sides to afford the closest agreement between the natural frequencies along radial directions defined by the eight electrodes. Further, frequency degeneracy may be obtained by simply sanding appropriate regions of lip 14. Bell B of FIG. 1 is thereby tuned to have a basic natural frequency of 2,100 Hertz with the difierence in frequencies along all radial directions degenerating to 0.03 Hertz or less.

Housing 90 is comprised of a top surface 92 supporting central hub 91 having port 97 therethrough and axially-extending cylindrical sides 93 terminating in flange 94 at its open end. Holes 95 through flange 94 allow the insertion of bolts 96 to secure housing 90 to radial surface 84 of platform 12, and an O ring 89 enables proper sealing between the platfonn surface 84 and housing flange 94. After such sealing, the application of a vacuum or the insertion of desirable gases is effected through port 97 which is thereafter sealable by means of plug 99 and washer 98. Air may thus be withdrawn from housing 90 through port 97 so as to increase the Q of bell 10 by decreasing air damping. For instance, it has been found that by maintaining the bell in a vacuum on the order of 10' torrs increases the Q of the device fourfold and hence comparably increases the time constant, or ringing time, of oscillations in relation to the energy input per cycle.

GENERAL OPERATION FIG. 1a

As may be understood generally with reference to FIG. 1a, the operation of bell B requires that sides thereof be exercised or forced radially so as to flex lip 14 between two extreme positions, shown in the dotted and dashed lines, about a neutral unflexed circular position, shown by the solid line. These exercising vibrations establish a standing wave pattern about the circumference of the lip. This pattern defines nodal regions of normally quiescent radial vibrations and anti-nodal regions of normally maximum radial vibrations, the location of these regions being defined when the bell is not rotated about the ZZ input axis.

Such flexing is initiated and sustained by an electromechanical self-oscillation loop comprised generally of forcer 42, sensor 54, and feedback means 101 located operatively about the sides of the bell, the bell in turn being connected to source of constant potential such as ground or otherwise. The forcer 42 is energized at a potential varying at the natural frequency of the bell to vary the potential difference between the sides and forcers creating therebetween a varying electrostatic force of attraction. This attractive force flexes lip 14 in a standing wave pattern having a set of antinodal regions 14a-14c and 14c-14g, respectively, along each of two mutually perpendicular directions AF-AF and APAP radial to the input or polar axis Z-Z and a set of nodal regions 14b-l4f and 14d-14h, respectively, along each of two mutually perpendicular directions NF-NF and NP-NP midway between those associated with the anti-nodes.

Deflections of the lip are detected by the sensors located adjacent thereto and measuring either the varying capacitance or varying potential therebetween depending on the input impedance of the circuits connected with the sensors. A sensor 54 located at anti-nodal region 14g detects the amplitude of radial vibrations of lip 14 antinodes. Electrical feedback means 101 connect sensor 54 to forcer 42 located at antinodal region 14a thereby closing a loop operative to flex the anti-nodal lip regions at constant maximum amplitude.

Other sensor means 52 located at nodal lip region 14f detect those radial vibrations at nodal regions due to the motion of the lip associated with the standing wave pattern and the rotation of the bell B about its input axis, such nodal vibrations believed to be due to the effect of Coriolis forces. Sensor 52 is connected to readout circuit 103 and develops in conjunction therewith signals usable for indicating the rate and direction of bellrotation and for energizing nulling forcer 48 located at a lipnodal region 14d to impart radial vibrations thereat substantially nulling the radial vibrations detected by sensor 52.

A key feature of the nodal and anti-nodal regions of the vibration pattern imparted and maintained by forcer 42 and sensor 54 is that radial vibrations produced along the antinodal AFAF and AP-AP directions cause the bell B to produce substantially no radial vibrations along nodal directions NF-NF and NP-NP. Similarly, and essential to the operation of the device, radial vibrations imparted along the nodal directions produce substantially no effects along the anti-nodal directions. In terms of the present invention, the vibrations imparted by nulling forcer 48 at nodal region 14d causes substantially no additional vibration to be detected by anti-nodal sensor 54.

Thus, the radial vibrations along the nodal directions are thus independent of those along anti-nodal directions in the absence of input rotation and vice versa, such independence also known mathematically as orthogonality. The benefit of this orthogonality feature is that the anti-nodal vibrations do not couple into the nodal sensor so that the nodal sensor and read-out electronics can operate very linearly with inputproduced nodal vibrations, thereby afiording maximum readout sensitivity. Another benefit of orthogonality also enhancing sensitivity is that input-caused nodal vibrations do not couple into the anti-nodal sensor and therefore render readout sensitivity substantially independent of variation in anti-nodal amplitude with variations in nodal amplitude.

Another feature inherent in the imparted radial vibration pattern and employed in the present device is that radial vibrations along any one anti-nodal axis are mathematically and substantially physically identical in magnitude and frequency to those along any other anti-nodal axis even though such axes are physically separated, and radial vibrations along one nodal axis are similarly identical to those along any other nodal axis even though physically separated. The effect of this feature is that all nodal and anti-nodal axes may be considered as equivalent respectively to just one nodal and one anti-nodal axis. Thus, radial vibrations produced at one nodal region by the imparted vibration pattern coupled with the Coriolis effects of rotation about the input axis appear identically at the other nodal regions with only the phase of the nodal vibrations being opposite depending on which region is being considered. Moreover, nulling radial vibrations imparted by a nulling forcer at one nodal region null] the input caused vibrations at the other nodal regions. Similarly, radial vibrations applied atone anti-nodal region produce substantially identical radial vibrations at the other anti-nodal regions.

DESCRIPTION OF OPERATION FIG. 2

The general operation and interconnecting of a self-oscillator loop and readout loop for respectively effecting vibration and detecting rotations in the present invention may be understood with reference to FIG. 2, a more detailed description of circuits for effecting these loops being presented below with reference to FIGS. 3 and 4.

The means comprising the self-oscillation and readout loops are shown interconnected in block form in FIG. 2 with electrode assembly 40 shown in plan view using like designations for similar elements in FIG. 1. Thus, electrode assembly 40 is disposed between post 24 and lip 14 as shown, and is comprised as described above of shield hub 58, shield spokes 60, guard web 64, guard arms 66, and electrodes 42, 44, 46, 48, 50, 53, 54, and 56.

The FIG. 2 self-oscillator loop is comprised generally of lip regions 14c and 14g of bell B, electrodes 46 and 54, oscillator pickoff amplifier 100, level detector 102, amplifier 106, filter 108, dc-to-dc converter 110, demodulator 112, multivibrator 114, flip flop 116, oscillator forcer circuit 118, electrodes 42 and 50, and lip regions 14a and 14e.

Electrodes 42 and 50 are oscillator forcer electrodes connected in parallel to oscillator forcer circuits 118 and operative to impart radial exercising vibrations to hell B by applying varying attractive electrical potential at lip regions 14a and 14e along an anti-nodal forcing axis AF-AF normal to the polar or input axis Z--Z. Electrodes 46 and 54 are oscillator pickofi electrodes connected in parallel to oscillator pickoff amplifier and operative to detect radial vibrations of bell B by measuring the varying potential with respect to fixed electrodes at lip regions 14c and 14g along an anti-nodal pick off axis AP-AP normal to both the AF-AF and 2-2 axes.

The output of oscillator pickoif amplifier 100 is connected parallely both to level detector 102 and to demodulator 112. A source of adjustable reference potential 104 is also connected to an input terminal of level detector 102, the output of which is connected to dc-to-dc converter through amplifier and compensator 106 and filter 108 to regulate the amplitude of the exercising wave. Demodulator 112 is connected to multivibrator 114 and therefrom to both converter 110 and to frequency dividing flip-flop 116. Synchronization pulses are provided by flip-flop 116 back to demodulator 122, to oscillator forcer circuit 118, and also to chopping modulator 128 in the readout loop. The output of demodulator 112 regulates the frequency of multivibrator 114 driving frequency dividing flip-flop 116, which in turn slaves at substantially the resonant frequency of lip 14 both the frequency of demodulator 112 and the frequency with which oscillator driver 118 applies a forcing potential to electrodes 42 and 50.

At start-up, the difference in amplitude between reference potential 104 and the signal from amplifier 100 corresponding to the maximum amplitude of lip 14 at regions 14cand 143 is of sufficient magnitude and a polarity to cause an output from dc-to-dc converter 110 to oscillator forcer circuit 118. The amplitude and frequency of the varying potential to oscillator forcer electrodes 42 and 50 and lip regions 14a and 14e therefore tends to increase the amplitude of lip vibrations. As the amplitude of lip vibrations increase, the input to detector 102 increases the difference from that provided by reference 104; The output from level detector 102 to converter 110 consequently increases to ultimately stabilize at a value corresponding to a substantially constant maximum amplitude of lip variation, such amplitude being adjustable by setting reference potential 104.

Free running multivibrator 114 is biased at start-up to operate converter 110 and to cause the output from frequency divider 116 to oscillator forcer circuit 118 to be less than the resonant frequency of lip 14. Thereafter, the bias to multivibrator 114 is adjusted by the output of demodulator 1 12 to effect a frequency which produces a maximum amplitude at lip 14 for the converter-regulated forcing potential. The output of multivibrator 114 is also applied to monostable vibrator 132, wherein the pulses from 114 are phase shifted by adjustment means 134 and then applied to demodulator 122 after frequency division by flip-flop 136.

The readout loop is comprised generally of lip regions 14b and 14f of bell B, readout pickoff electrodes 44 and 52, readout summing amplifier 120, demodulator 122, phase shifting monostable vibrator 132, frequency dividing flip-flop 136, compensator amplifier 124, chopping modulator 128, amplifier 130, readout forcer circuits 138, readout forcer electrodes 48 and 56, and back to lip 14 at regions 14d and 14h.

Electrodes 44 and 52 are readout pickoff electrodes connected in parallel to readout summing amplifier 120 and operative to detect radial vibrations of bell B by measuring the varying potential at lip regions 14b and 14f along a nodal pickoff axis NP-NP between AF-AF and AP-AP axes. Similarly, electrodes 48 and 56 are readout forcer electrodes connected in parallel to the output amplifier 130 and readout forcer circuit 138 and operative to impart radial vibrations of proper frequency and amplitude to bell B by applying varying attractive potential at lip regions 14a and 14b along nodal forcing axis NF-NF between the AP-AP and AF-AF axes and normal to the NP-NP axis to null the vibrations sensed by readout pickoff electrodes 44 and 52.

The output of readout summing amplifier 120 is connected to demodulator 122, the output of which after amplification and compensation in amplifier 124 provides a signal at 126 proportional to the rate of rotation of bell B about axis of symmetry Z-Z. Signal 126 may also be used to energize means (not shown) generating pulses that can be counted to indicate the amount of rotation about axis Z-Z over a given period of time, thereby indicating angular displacement of bell B about axis Z-Z.

The output of amplifier 124 is also chopped or modulated in the present embodiment at a frequency determined by the output of flip-flop 116 to provide a varying potential from amplifier 130 that is summed at node 140 with a regulated DC potential from readout forcer circuit 138 energized by the output of dc-to-dc converter 110. The forcing potential subsequently applied to electrodes 48 and 56 is a dc bias that is augmented by a potential having an amplitude proportional to the input rate, a frequency determined by multivibrator 114 and flip-flop 116 to be substantially the resonant frequency of lip 14, and a phase of 180 opposite to the vibration of lip regions 14b and 14f.

FIG. 3 DESCRIPTION OF OPERATION With reference now to a more detailed electrical schematic of the means for effecting the vibrations in the lip 14 of the bell B and detecting rotations thereof, there are shown in FIG. 3 a plurality of operational amplifiers A2, A4, A6, A8, A10, A12, A14, and A16, with two more such amplifiers (not shown) incorporated in readout pickoff amplifiers 117 and 119. These amplifiers are UA709 integrated circuit units available from the Fairchild Semiconductor Corporation, or the equivalent, and are connectable in a variety of modes for effecting variable gains, phase inversions, and difierential action. Signals to one input terminal (IN) of each such amplifier causes an inverted output therefrom at the circuit connected to the apex of the triangular symbol, and signals to another input terminal (NI) causes a noninverted output. The gain through each amplifier is determined in part by the impedances in the feedback loop, if present. Each amplifier has terminals for applying positive and negative energization and for effecting frequency compensations. Typical of such energization and compensation connections are those shown for amplifier 101'. As shown therein, amplifier A4 has inverting and non-inverting input terminals IN and NI, respectively. Plus and minus 12 volt supplies are connected through resistors R10 and R11, as indicated, with capacitors C5 and C6 serving to define filters. Internal oscillations are neutralized through resistor R9 and capacitor C3, and input-tmoutput phasing is controlled by capacitor C4.

PICKOFF AMPLIFIER Amplifier 100 is schematically representative of the pickoff amplifiers 101, 117, and 119. These amplifiers associated with the self-oscillating loop and with the readout loop and are identical except that the feedback resistors R6 for oscillator pickofi amplifiers 100 and 101 are substantially smaller than feedback resistor R6 for the readout pickoff amplifiers 117 and 119, in order to effect a higher gain and readout sensitivity from the latter.

Pickoff amplifier 100 is composed of two stages. The first stage, having a gain of one, is composed of field effect transistor T2, transistor T4, 3.9 volt Zener diode Z2, capacitor C1, and resistors R1, R2, R3, R4, and R5. The second stage, having a gain of two, is composed of amplifier A2, capacitor C2, and resistors R6, R7, and R8.

In the first stage, resistor R1 is connected between the oscillator pickup electrode 46 and the gate of field effect transistor T2, the source terminal of which is connected to the plus 12 volt supply across R5 and the drain terminal of which is connected to the base of transistor T4. To provide a suitable voltage difference between the bell B and the electrodes, a 45 volt dc supply E is connected with its positive terminal to hell B and its negative terminal to the T4 collector and the non-inverting input of amplifier A2 across resistor R8. Resistors R2 and R3 are connected between the T2 gate and negative terminal of supply E as shown.

A field effect transistor is used for T2 in this stage as elsewhere hereinafter because of its inherently low power requirements and because of its inherently negligible zero bias-offset characteristics with zero signal. To connect T2 to operate in a boot-strapped source-follower mode and to effect bias between the T2 source and drain terminals, Zener Z2 is connected thereacross via the T4 emitter-to-base junction. Transistor T4 is operated class A (Le, linear output with input), and T4 emitter is AC coupled to the node between resistors R2 and R3 by capacitor C1 and resistor R4, as shown, to feed the T4 emitter output signal back to the relatively large R resistance R1 (1.8 megohm) to provide negative feedback. The input impedance effect of R2 is multiplied by this feed back to afford an overall input resistance of approximately 50 to I00 megohms to the first stage. Such high input impedance renders the bell B, (FIG. 1), effectively at a constant charge relative to the amplifier 100 input. This in turn causes deflections of lip 14 to be detected as changes in voltages on electrodes 46 and thereby affords better detection sensitivity than if amplifier A2 had a low input impedance and consequently measured change of capacitance with lip deflection. Moreover, to render electrode 46 insensitive to the eflect of lead-in and other spurious capacitances, guard 66 is also connected to the node between resistors R2 and R3 as shown so that the above-mentioned feedback from the T4 emitter is employed to vary the potential on guard 66 in phase with that on electrode 46. The effect is to substantially eliminate any substantial potential difference between electrode 46 and guard 66, thereby establishing a small but constant capacitance cage around all of the surfaces of electrode 46 except that arcuate surface exposed to the varying potential caused by movement of the lip 14.

The T4 emitter output of the first stage is also AC coupled by capacitor C2 to the inverting input terminal of operational amplifier A2 via input resistor R7. The A2 output is coupled by capacitor C7 to the input of level detector 102 and demodulator 112. Feedback resistor R6 connected across the A1 input and output terminals is selected to be substantially twice R7 so that the voltage gain of the second stage is two. Since the voltage gain of the first stage is one and of the second stage is two, the voltage gain through amplifier 100 is therefore also two.

The operation of amplifier 100 is controlled by the potential on the gate of FET T2, this potential varying in accordance with the magnitude of the gap between electrode 46 and lip region 14c of bell B. However, due to the high A2 input impedance mentioned above, substantially no current flows through resistor R1 so that the low side of source E is applied to the gate of FET T2 across R2 and R3 when lip 14 is in its neutral or unflexed position. As the lip region 14c approaches electrode 46, the potential therebetween increases linearly due to the constant charge of bell B and the energy density between the bell B and the electrode 46. The energy density D may here be expressed equal to QV/2Ad, where Q in this formula is the Coulomb charge on the bell B, V is thepotential difference between the bell and the electrode, A is the effective common area of facing surfaces of bell B and the electrode, and d is the distance therebetween. Thus, rearranging this expression so that V DZAd/Q and assuming charge Q constant due to a high input impedance to amplifier A2 and a constant potential applied to hell B,-it may be seen that the voltage V is directly proportional by a constant K to the separation d, so that V Kd. The signal supplied to the gate of PET T2 from electrode 46 across resistor R1 therefore varies with the instantaneous amplitude of lip 14c oscillation and a drive signal varying correspondingly is applied from the drain terminal of T2 to in turn develop a similarly varying signal at the T4 emitter.

LEVEL DETECTOR 102, REFERENCE 104, AND AMPLIFIER 106 Level detector 102 is comprised of diode D2, capacitors C8 and C9, and resistors R20 and R21. Capacitor C8 decouples the dc portion of output from amplifier 100 and resistor R20 blocks frequency effects that would otherwise be propagated backwardly by the chopping action of demodulator 112, the operation of which will be described below. Diode D2, capacitor C9, and resistor R21 comprise an AM detection stage for detecting a signal proportional to the maximum amplitude of the varying voltage produced on electrode 46 by the motion of lip 14. in this stage, diode D2 rectifies the output of the C8/R20 input filter to provide a uni-polarity signal suitable for amplitude detection by a filter comprised of resistor R21 and capacitor C9. The signal thus detected by the C9/R21 filter is applied across input resistor R22 to the inverting input terminal of amplifier A6 in amplifier and compensating circuit 106. The non-inverting input terminal of amplifier A6 is connected to a reference circuit 104 comprised of adjustable resistor R28 maintained with a constant drop thereacross by 6- volt Zener diode Z4, the parallel combination of Z4 and R28 being connected from a plus 12 volt supply to ground via resistor R30, as shown. The reference for non-inverting input terminal of amplifier A6 is connected to the wiper of adjustable resistor R28 across resistor R26.

Amplifier A6 is essentially a lower power device developing outputs on the order of millivolts and milliamps. However, since a higher power drive is needed for dc-to-dc converter 110 and the forcer circuits 118 and 138, the A6 output terminal is connected to the base of a signal boosting transistor T6. The T6 collector is connected to a plus l2-volt supply and the T6 emitter is connected to the inverting input terminal of amplifier A6 across feedback resistor R24 and also to ground across sampling resistor R32 and to the input terminal of dcdc converter 110.

Transistor T6 is operative to amplify the difference in signals applied to the input terminal of amplifier A6 so as to provide a suitable current drive for dc-DC converter 110. To effect vibration of lip 14 at some desired maximum amplitude, the reference signal applied to the non-inverting input of amplifier A6 from reference resistor 28 is adjusted to provide some potential greater than the signal at the A6 inverting input comprised of the AM detection signal across input resistor R22 and the T6 emitter signal fed back across R24. The

. differential input to amplifier A6 when amplified by boosting transistor I6 and converted to a dc level by dcdc converter is effective to cause forcer circuit 118 to apply a suitable potential to forcer electrodes 42 and 50 so as to flex lip 14 at the desired amplitude. Should this amplitude for some reason be less than normal, as for instance in start-up, the differential input to amplifier A6 would increase in a positive sense due to a lower output from the C9/R21 detector filter. This in turn would increase A6 output and the base drive to transistor T6, ultimately increasing the amplitude of lip vibration. Conversely, should the amplitude of lip 14 vibration be greater than normal, as for instance the result of too great an-output from the dcdc converter 110, the differential input to amplifier A6 would decrease to in turn decrease the output therefrom and ultimately the drive to the dcdc converter 110.

DC-DC CONVERTER 110 Dc-dc converter 110 is comprised essentially of a pushpull blocking-oscillator stage and a bridge rectifier stage. The blocking oscillator in turn is comprised of primary and secondary transformer windings L4 and L6, transistors T8, T10, and T18, biasing resistors R34 and R36, start-up resistors R59 and R62, start-up diodes D4, D14, and D16. The rectifier stage is comprised of bridge diodes D6, D8, D10, and D12.

In the blocking oscillator stage, the center tap of primary winding L4 is grounded, and an emitter tap on either side of the ground tap is connected to respectively the emitters of pushpull transistors T8 and T10. Flyback winding portions of L4 are wound oppositely to the L4 portions between the center and emitter taps and are connected to the T8 and T10 bases respectively across biasing resistors R34 and R36. Then, with the T8 and T10 collectors connected commonly to a source of positive potential developed at the output of amplifier 106, transistor T10 is biased into conduction by a positive potential applied to the T10 base from multivibrator 114 via transistors T18 and diode D14 or from the L4 flyback tap across R36. This causes the circuit to ultimately regenerate or bootstrap itself into a blocking oscillation mode. Assuming for descriptive purposes that conduction through T10 has just commenced and that through T8 has just terminated, in this mode current would flow from the T10 collector-to-emitter junction through primary winding L4 to ground. As the potential induced at the T10 emitter tap thus increases, with increasing T10 conduction, the potential at the associated flyback tap decreases, thereby decreasing the forward bias to T10 and ultimately cutting it off. Conversely, as the potential at the T8 emitter tap decreases, that at the T8 flyback tap increases, thereby biasing T8 into conduction as T10 is cut off. This process is then reversed and recycled to ultimately effect blocking oscillation with transistors T8 and T10 switched at a frequency determined primarily by the circuit inductances and resistances. For the component values used in the FIG. 3 converter, this frequency is on the order of 8KC, and the switching noise generated thereby is blocked by choke L2 and capacitor C11 from propagating backwards to amplifier 106 to enhance the stability and accuracy thereof.

To initiate the switching, the T10 base is connected to an output of free-running multivibrator 1114 via the emitter-tocoUector junction of transistor T18 and diode D14. At start-up the T18 emitter-to-base junction is forward biased from the minus l2-volt supply across resistor R59, and multivibrator 114 is biased from the plus 12-volt supply across resistor R56 to generate 8KC positive pulses of sufficient magnitude to bias T and effect blocking oscillation. In view of the start-up potentials diode D4 is connected forwardly between resistor R36 and T10 base to prevent the T10 emitter-to-collector junction from the reverse voltage effects of pulses developed by free-running multivibrator 114 during start-up. On the other hand, to protect the T18 collector-to-emitter junction from the reverse effects of the flyback voltages to the T10 base during normal operation, diode D14 is connected forwardly between the T18 collector and the T10 base. Finally,

Resistor R52 and capacitor C14 are connected in feedback from the output terminal of amplifier A8 to the inverting input terminal thereof. The gate to FET T16 is driven from one synchronizing output of flip-flop 116 to promptly ground the inverting input to amplifier A8 while such input as developed by amplifier 100 is negative. The non-inverting input terminal to amplifier A8 is effectively grounded by resistor R54, as shown.

The output developed by amplifier A8 is summed with that diode D16 is connected forwardly from the T18 base to the 10 developed across resistor R56 connected to the plus l2-volt negative supply across resistor R59 to effectively cut off the forward bias to T18 when converter 110 develops an output sufficiently positive voltage across resistor R62 to reverse bias D16.

The output taps of secondary winding L6 are connected to a bridge rectifier comprised of high side diodes D6 and D8 and low side diodes D10 and D12, as shown. The output of dc-dc converter 110 is applied from the cathodes of high side diodes D6 and D8 to oscillator forcer circuit 118 and readout forcer circuit 138, providing a DC supply bias thereto varying in accordance with the maximum amplitude of lip 14. In the present circuit this bias varies from about 250 volts at start-up to about 400 volts at normal resonant operation.

OSCILLATOR FORCER CIRCUIT 118 Oscillator forcer circuit 118 is comprised of transistors T20, T22, T24, and T26, capacitors C16 and C18, and resistors R57, R58, R59, R60, R62, R64, and R66. As shown, the base of transistor T20 is connected to one output of flip-flop 116, and the T20 emitter is grounded. The T20 collector is biased from a plus 12-volt supply via R57 and is also connected respectively to the base of T22 across capacitor C16 and resistor R58 in parallel and to the base of T26 across capacitor C18 and resistor R60 in parallel. The collector of transistor T24 is connected to the output of dc-dc converter 110 and also to the minus 12-volt supply across resistors R59 and R62. Resistor R64 is connected between the collector and base of transistor T24. The T24 emitter is connected both to the T26 collector and to electrodes 42 and 50 in parallel. The T22 and T26 emitters are grounded.

Transistors T20 cooperates with transistors T22 to switch transistors T24 and T26 in a complementary mode so that when T24 conducts T26 does not and vice versa. Due to the necessity of providing precise potentials to the electrodes 42 and 50 at the resonant frequency of the system, the switching of transistors T24 and T26 must be rapid and accurate. Transistor T26 assures a rapid sweep out of the charges in the junctions of transistor T24 to promptly cut off the potential to the electrodes 42 and 50. To effect this, a pulse from flip-flop 116 causes a positive signal to appear on the T20 base across input resistor R66. This biases T20 into conduction, thereby grounding the T20 collector and in turn the bases of transistors T22 and T26 to terminate conduction therethrough. With transistor T20 conduction and transistors T22 and T26 off, the output of dc-dc converter 110 biases the T24 base across R64 into full conduction so that the potential developed by dc-dc converter 110 appears at emitter T24 and in turn at the forcer electrode 42 and 50. When the pulse from flip-flop 116 falls to cut off transistor T20, the plus supply voltage appears at the T20 collector to bias transistors T22 and T26 into conduction. With transistors T22 and T26 on, the base of transistor T24 is grounded through the T22 collector-to-emitter junction so that the T24 is cut off at the same time that its emitter is grounded through the T26 collector emitter junction.

DEMODULATOR 112 Demodulator 112 is comprised of amplifier A8, capacitor C14, field effect transistor T16, and resistors R48, R50, R52, and R54. One end of A8 input resistor R48 is connected to the output of amplifier 100 and the other end is connected both to supply and is then applied as a bias to free running multivibrator 114 to determine the frequency of pulses produced therefrom. With the vibration signal developed at the output of pickoff amplifier grounded at the inverting A8 output terminal during the negative half cycle by the synchronized action of PET T16 and with such signal applied to the invening input terminal of amplifier A8 during the positive half cycle, amplifier A8 develops a negative output signal that is also filtered by feedback resistor R52 and capacitor C14 to remove the noise effects of switching FET T16. Resistor R52 and C14 also provides phase compensation to the self-oscillator loop so that the A8 output is proportional to the amplitude of lip vibration times the cosine of the phase difference of the lip vibrations and the output of multivibrator 114, thereby locking the phase of the self-oscillation loops to that of the lip vibrations.

MULTIVIBRATOR 114 As known in the art, a loop when in self-oscillation has a unity gain therethrough. Moreover, at start-up this gain is greater than one so that after the loop circuits are energized from the plus and minus l2-volt supplies as shown, any slight environmental vibrations imparted to the lip 14 or electronic noise in the loop circuits causes the system to regenerate toward resonant oscillation. As the amplitude of lip vibration is increased thereby, the loop gain falls toward unity. This is due to non-linear loop elements exhibiting reduced gain with increased amplitude, such elements here including amplifier 100, level detector 102 and amplifier 106.

The frequency of lip vibration at which the lip amplitude effects a self-oscillating loop having unity gain coincides substantially with the resonant frequency of the loop circuits; the frequency of the loop circuits, however, is determined and synchronized by the output frequency of multivibrator 114. At start-up, this output frequency is determined primarily by the positive bias applied to multivibrator 114 from the plus 12- volt supply across R56. After start-up, this positive bias is reduced by the increasingly negative output developed by amplifier A8 as the lip amplitude increases. Since the lip amplitude stabilizes at some magnitude effecting unity loop again as just discussed, the negative A8 output also stabilizes at some magnitude, and this magnitude when summed across resistor R55 with that from the plus l2-volt supply across resistor R56 ultimately stabilizes the frequency of the output pulses from multivibrator 1 14 at the resonant frequency of the system.

SUMMING AMPLIFIER Readout summing amplifier 120 is comprised of readout pickoff amplifiers 117 and 119, operational amplifier A10, and resistors R83, R84, and R85. Pickoff amplifiers 117 and 119 provide a gain of 100 therethrough and are of configuration as described above with respect to oscillator pickolT amplifiers 100 and 101 and have their input terminals connected respectively to electrodes 44 and 52 in proximity to nodal lip regions 14b and 14f. The output terminals of amplifiers 117 and 119 are connected in parallel to and thereby summed at the inverting input terminal of amplifier A8 across input resistors R83 and R85. To efiect voltage division with R83 and R85 so as to average the summed inputs, resistor R84 is connected in feedback between the A10 input and output terthe source terminal of FET T16 and to A8 input resistor R50. 75 minals.

Connected in the electrode configuration and circuit shown, the inputs to amplifier A developed by readout pickofi amplifiers A120 and 121 are in phase and, therefore, averaged by amplifier A10 through the voltage division performed by resistors R83, R84, and R85. The output signal developed by amplifier A10 varies with the amplitude and frequency of vibration at nodal lip regions 14b and 14f and is either the same or opposite phase as vibration of lip regions 14a and 14c depending on the direction of rotation of bell B about axis Z--Z.

DEMODULATOR 122 Demodulator 122 is comprised of amplifier A12, field effect transistors T32 and T34, capacitors C24, C25, and C26, and resistors R88, R90, R92, R94, and R98. These are connected to effect a chopping or demodulation stage and a unity gain filtering stage. In the chopping stage, the output terminal of summing amplifier 120 is connected across capacitor C14 to decouple the dc and then in parallel across series input resistors R88 and R94 to the inverting input terminal of amplifier A12 and across input resistors R90 and R92 and A12 noninverting input terminal. The node between resistors R88 and R94 is connected to the source terminal of FET T32 and the node between R90 and R94 to the source of PET T34. The drain terminals of FETs T32 and T34 are grounded and their gate terminals are connected to complementary outputs of flip-flop 136. Gated from flip-flop 136, FETs T32 and T34 alternately ground the A12 inverting and non-inverting input terminals so as to provide a dc signal at the A12 output terminal. To filter the noise effects of switching FETs %32 and T34 from the A12 output, resistor R98 and capacitor C26 are T32 between the A12 output and inverting input terminals, and resistor R96 and capacitor C25 are connected for the same reason from the non-inverting A12 input terminal to ground. Moreover, to effect unity gain through A12, feedback resistor R98 is selected equal to the series input resistors R88 and R94 or R90 and R92.

The output developed at the A12 output terminal is of an amplitude proportional to the magnitude of the input rate to bell B about axis Z-Z and of positive or negative polarity depending on the sense of the input rate. For example, connected as shown in FIG. 3, the circuit is phased so that the A10 output varies in phase with that of anti-nodal lip regions 14a and 14c for clockwise rotation of bell B and so that the A12 output is then positive. Positive excursions of the A10 output are then applied to the non-inverting A12 input terminal and negative excursions of the A10 output are applied to the inverting A12 input. Since FET T34 grounds the A12 input during the positive excursions of the A10 outputs and PET T32 during negative excursions, the signal developed at the A12 output terminal in this case is positive for both positive and negative excursions of the A10 output.

Conversely, should the input rate now be counterclockwise, the A10 output would be out of phase with the vibrations of anti-nodal lip regions 14a and 140. Positive A10 output excursions would then be applied to the inverting input of amplifier A12 to produce a negative output therefrom at the same time that the non-inverting input is grounded through FET T32. Half a cycle later when the A10 output goes negative, A12 inverting input is grounded by FET T34 so that the negative signal to the non-inverting A12 input produces a negative output therefrom.

COMPENSATION AMPLIFIER 124 Compensation amplifier 124 is comprised of amplifier A14, capacitors C27 and C28, resistors R100, R102, R104, R106, and R108. The output developed at demodulator 122 is applied across input resistor R100 to the inverting input terminal of amplifier A14 and the non-inverting input terminal 'is grounded. The A14 output terminal is connected to the A14 inverting input terminal in parallel by feedback resistor R102, by a filter comprised of series resistors R104 and capacitor C28, and by capacitor C27. The effective parallel resistance of resistors R102 and R104 is selected to be times greater than input resistor R100 to provide a gain of 100 through amplifier A44. This gain when combined with the gain of 100 through pickoff amplifiers 117 and 119 provides a readout loop gain of 10,000. The effect of resistor R104 and capacitors C27 and C28 is to decrease this gain linearly from zero to 10 cycles and to render it constant over a bandwidth from 10 to 250 cycles a second, thereby rendering the readout linearly sensitive to input rates out to 250 cycles per second. However, this bandwidth is narrowed as the non-degeneracy between the oscillation and readout frequencies increases.

The signal developed at the A14 output terminal is a dc signal the magnitude of which varies with the rate of input rotation and the polarity of which is plus or minus depending upon the direction of inputs. Amplifier A14 is adjusted to provide a zero output for a zero input by means of variable resistor R106 connected across resistance R108, and energized from the minus 12-volt supply, as shown. Modulator 128 chops the output of amplifier 124 to provide pulses of varying magnitude to drive electrodes 48 and 56.

MODULATOR 128 AND AMPLIFIER 130 Modulator 128 is comprised of field effect transistors T36 and T38, amplifier A16, resistors R110, R112, R114, R116, R117, R118, and R120, and capacitor C30. The output terminal of compensation amplifier 124 is connected in parallel across series input resistors R110 and R114 to the inverting input terminal of amplifiers A16 and across series input resistors R112 and R116 to the A16 non-inverting terminal. The node between resistors R110 and R114 is connected to the source terminal of PET T36, and the node between R112 and R116 to the source of FET T36. The gate terminals of FETs T36 and T38 are connected to complementary outputs of flipflop 116 and the drains of these FET s are grounded. Resistor R118 connected between the A16 input and output terminals is chosen substantially equal to the summed values of R110 and R114 to effect unity gain through amplifier A16. Resistor 117 is also connected to the non-inverting input of amplifier A16 to provide voltage division of the input thereat. Resistor 120 and capacitor C30 connected in series to electrodes 48 and 56 respectively serve to provide output pulses thereto and to isolate the output of amplifier A16 from the dc output of forcer circuit 138, to be described shortly below. The magnitude of the output pulses developed by amplifier A16 across R120 is summed with the output of converter 110 as regulated and attenuated by readout forcer circuit 138.

READOUT FORCER CIRCUIT 138 Readout forcer circuit 138 is essentially a series regulator comprised here of transistors T12 and T14, Zener diode Z6, resistors R40, R42, R44, and R46, and capacitor C12. The high-side output of dc-dc converter 110 is connected to the collector of T12 and to the base thereof across resistor R40 and the T12 base is also connected to the collector of transistor T14. The T14 emitter is kept at constant potential by 10-volt Zener Z6, the cathode of which is connected to the plus 12-volt supply across resistor R46 and the anode of which is grounded. The emitter of transistor T12 is connected in parallel by capacitor C12 and resistor R42 to the T14 base of T14 which is then grounded across resistor R44. Transistor T12 is forward biased by the output of the converter 110 at the T12 collector and the 10-volt Zener reference at the T12 base via T14 collector to emitter junction. Transistor T14 is in turn forward biased by the T12 attenuated converter potential on the T12 emitter connected to the T14 base via C12 and R42. Fluctuations in the converter potential are coupled to the T14 base via capacitor C12 altering the T14 bias, the conduction through T14, and in turn the T12 bias. For example, a momentary increase in the output from converter 110 would increase the T12 emitter potential to increase the forward bias on T14, thereby reducing the T12 bias and reducing the gain through T12. The result is that the T12 emitter potential is regulated at 200 volts and this potential is summed at 140 with pulses of up to 20 volts peak-to-peak produced by modulator 130, any effect of these pulses on forcer circuit 138 being blocked by resistor R38.

TIMING CIRCUITS AND WAVEFORMS Timing and synchronization of the FIG. 3 circuits is obtained through multi-vibrator 114 discussed above, monostable vibrator 132, flip-flops 116 and 136, and diodes D22, D24, and D26. The operation of these conventional units will be discussed with reference to the waveforms in FIG. 4, wherein waveforms WF2, WF4, WF6, and WF8 are associated generally with the self-oscillator loop and waveforms WF 10, WF12, WF14, WF16, WF18, WF20, WF22, WF24, WF26, and WF28 are associated generally with the readout loop. The scale of waveforms WF2, WF8, and WP 18 is in inches, that of WF28 in volts and the remainder in millivolts.

Waveform WF2 represents the displacement between antinodal lip region 14c and oscillator sensor electrode 46; and waveform WF4, the zero-phased output of output multivibrator 114 and also the start-up bias to the base transistor T10. Waveform WF6 represents the zero-phased a output of flip-flop 116, and therefore the variation in potential difference between anti-nodal lip region 14a and oscillator forcer electrode 42. By representing the periods during which the inverting input terminal to amplifier A16 is grounded and not grounded, waveform WF6 also represents the complementary grounding and non-grounding of the A16 inverting input terminal. Wavefon'n WF8 represents the displacement between anti-nodal lip region 14a and oscillator forcer electrode 42.

Waveform WF10 represents the pi-phased (i.e., 180 electrical degrees from the zero phase) output of multivibrator 114; and waveform WF12, the output of monostable vibrator 132 displaced in phase by some angled: from the fall of the piphased output of multivibrator 114, waveform WF10. Waveform WF 14 represents the zero-phased output of flipflop 136 and therefore the periods in which the non-inverting input terminal to amplifier A12 is grounded and not grounded, and waveform WF 16 represents the pi-phased output flip-flop 136 and also the periods in which the inverting terminal to amplifier A12 is grounded and not grounded.

Waveform WF18 represents the displacement of nodal lip reion 14b from readout sensor electrode 44 for counterclockwise rotations of platform 12 around the input axis Z-Z. Waveform WF20 represents the signal developed at the output terminal of summing amplifier 120 as rate signal 126. Waveforms WF22 and WF24 respectively represent the outputs of demodulator 122 and compensation amplifier 124. Representing the pi-phased output of flip-flop 116 and also the periods in which the inverting terminal to amplifier A16 is grounded and not grounded, waveform WF26 also represents the complementary grounding and non-grounding of the noninverting A16 input terminal. Finally, waveform WF28 represents the variation in potential difference between nodal lip region 14d and readout forcer electrode 48.

Timing signals for both the oscillator and readout loops are initiated by and slaved to generally the zero and pi-phased output pulses, waveforms WF4 and WF10, produced by free running multivibrator 114. As has been described above, multivibrator 114 synchronizes the oscillator loop by providing starting pulses to converter 110 and by clocking flip-flop 116 which in turn generates zero-phased pulses that synchronize both demodulator 112 and forcer circuit 118. While in the ideal case the zero and pi-phased pulses from flip-flop 116 could also serve to synchronize the readout circuits, phase shifts between the oscillator and readout loops could render the demodulation readout signal inaccurate. Such phase shifts develop from slight differences in frequency and phase of the vibrations of the bell lip along the nodal axes relative to those along anti-nodal axes and also from the circuits comprising the oscillator loops relative to the circuits comprising the readout loop. Such phase differences are accommodated in the present rotation detector so that the readout detected is a maximum for a given input about the Z-Z axis. For this purpose, the functions of free running multivibrator 114 and frequency-dividing flip-flop 116 for the oscillator loop are in essence duplicated by monostable vibrator 132 and flip-flop 136 for the readout loop with phase adjusting means 134 (variable resistor R72) introducing the necessary phase difference between the loops. More specifically, the pi-phased output of multivibrator 114 is applied to monostable vibrator 132 and phase shifted therein by means of adjustable resistor R72 to provide an output waveform WF12 to clock flip-flop 136, causing therefrom zero and pi-phased outputs WF14 and WF 16. The zero-phased 136 output WF 14 is applied to the gate of FET T32 and a pi-phased output to the gate of FET T34 to complementarily ground therethrough the non-inverting and inverting input terminals respectively of amplifier A 12 in demodulator 122. The effect of such complementary grounding is that signal developed at the output terminal of amplifier A10 of readout summing amplifier is applied to that input terminal of amplifier A12 that is not grounded. For instance, with a counter-clockwise rotation of the platfonn 12 about the Z-Z input axis, signals developed by pickofi amplifiers 117 and 119 corresponding to the displacement of lip 14b from electrode readout sensor 44 as shown in waveform WF 18 are summed at the inverting output terminal of amplifier A10 to produce inverted output WF20 therefrom. The zero-phased output from flip-flop 136 gates the negative halfcycles of the A10 output to the non-inverting input terminal of amplifier A12 producing a negative output therefrom, and the pi-phased 136 output gates the positive half-cycles of the A10 output to the inverting input terminal of A12 also producing a negative output signal. Thus, for the connection of electrodes, phasing, and input rotation described, a negative signal is developed at the A12 output terminal. This signal is applied to the inverting input terminal of compensation amplifier A14 to develop a positive output signal 126 as an indication of the magnitude and direction of the input about the Z-Z axis.

To convert the A14 output into pulses nulling input produced nodal vibrations, the zero-phased output from flipflop 116 is applied to the gate to FET T36 and the pi-phased output to the gate of FET T38 to complementarily ground the non-inverting and inverting input terminals of amplifier A16 in modulator 130. This gates the A14 output to that input terminal of A16 not grounded. The effect is to produce pulses at the output of amplifier A16 that vary in magnitude with the input rate and that add and subtract from the regulated potential supplied by readout forcer circuit 138 at summing node 140. Thus, again for the connection of electrodes, phasing, and direction of rotation described, the zero-phased 116 output gates the positive A14 output to the non-inverting A16 input terminal thereby adding variable amplitude pulses to the output from readout forcer circuit 138, and the pi-phased 116 output gates the positive A14 output to the inverting A16 input terminal, thereby subtracting variable amplitude pulses from the output of forcer circuit 138. The result at summing node 140 is pulsed potential of up to 20 volts peak to peak depending in magnitude on magnitude of the input rate, and this signal adds and subtracts from the regulated 200 volt output from forcer circuit 138. The phasing of these forcing pulses relative to the lip-electrode displacement shown in WF20 provides attractive forces between forcer electrode 48 and lip region 14d tending to oppose the displacement caused therebetween by the effects of input rotation on the lip vibration pattern. ln other words, the attractive potential is less during the half cycle that lip region 14d is nearest forcer electrode 48 than during the half cycle that region 14d is farthest from electrode 48. The effect of this forcing potential however is to oppose and in fact substantially null the nodal lip vibration. There being little if any displacement of nodal lip region 14d in actual operation, this description of the phasing of the forcing potential relative to lip 14d vibration is primarily for understanding.

To complete the synchronization of the oscillator loop with the readout loop, diodes D22, D24, and D26 are connected to perform a logical ANDing function to assure that the phase of oscillator and readout loops, and particularly flip-flop 136, is the same at each start-up and not 180 out of phase. The anodes of these diodes D22, D24, and D26 are therefore connected both to the zero-phased input of flip-flop 136 across capacitor C32 and to the plus 12 volt supply for flip-flop 136 across resistor R81. The cathode of diode D22 is connected to the zero-phased output of flip-flop 116; the cathode of D24, both to pi-phased input of flip-flop 136 via capacitor C31 and to the output of monostable 132; and the cathode of D26 to the zero-phased output of flip-flop 136. By the blocking action of these diodes so connected, the zero-phased 136 output is kept low via capacitor C31 and the pi-phased output high via capacitor C32 until both the output of monostable 132 and the zero-phased output of flip'flop 1 16 are high.

The following is a table of representative values of the components that may be used to construct and operate the circuit shown in FIG. 3 and discussed above:

TABLE OF FIGURE 3 COMPONENTS AND VALUES Value Value Resistor (R) (ohms) Resistor (ohms) 1 l meg. 56 3.6 K 2 1.8 meg. 57 4.7 K 3 6.8 K 58 2 K 4 2.2 K 59 200 K 470 60 2 K 6 20 K 62 2.2 meg. 6 1 meg. 64 510 K 7 K 66 51 K 8 10 K 72 51 K 9 1.5 K 81 10 K 10 100 83 100 K 1% 11 100 84 100 K 1% 20 10 K 85 100 K 1% 21 2 K 86 100 K 1% 22 l K 88 10 K 24 l meg. 90 10 K 26 100 K 92 100 K 1% 28 3 K 94 100 K 1% 30 680 96 100 K 1% 32 5.1 K 98 110K 1% 34 l K 100 360 36 l K 102 360 K 38 10 K 104 39 K 40 910 K 106 100 K 62 2.7 meg. 108 470 K 44 110 K 110 w-rt: watt. 112 10 K 48 10 K 114 100 K 1% 50 150K 116 100K 1% 52 K 117 100 K 1% 54 150K 118 ll0K1% 55 8.2 K 120 51 Value Diodes Type Zeners (Volts) 2 FD 333 2 3.9 v 4 PD 333 4 6 IN 3282 6 10 8 IN 3282 10 IN 3282 12 1N 3282 14 FD 333 16 FD 33 Capacitor Value Transistor Type I lp.f

at 35 v. 2 2N3976 2 l f at 35 v. 4 2N2605 3 0.005 #1 6 2N3404 4 200 pf 8 2N3415 5 6.8 at 10 2N34l5 6 6.8 pf 12 MST105 7 1 at 14 MST105 8 0.1 at 16 2N3820 9 6.8 .tf 18 2N3638 10 0.1 [Lf 22 M81705 11 6.8 pf 24 MST 705 12 0.01

at 600 v. 26 MST705 5 14 1.0 [if 32 2N3820 16 002 pt 34 2N3820 18 0.02 at 36 2N3B20 19 200 pf 38 2N3820 0.0047 #f 23 300 pf 10 24 0.0068 r 0.15 r 26 0.0068 r 27 0.02 nf 2a 0.33 pf 0.02

at 600 v. 15 31 300 pf 32 300 pf CONCLUSION 20 In the foregoing description and the appended claims, I have used the term bell" to describe generally a member having a ring portion and extending in a concave-convex configuration to a center point. Such member may be cup-like as herein specifically described, may be flared at the lip like a ships or churchs bell, or may even be in doubled form to define a sphere-like shape. In all of these shapes, a resilient ring portion capable of radial vibrations is provided and may be supported at the junction of the nodes and anti-nodes as described above.

In addition to rings and bells, hollow or even ball-type mediums wherein the radial vibrations are caused by substantially bending-type flexing action may be used. Also, even though the vibrations therein are caused by compression or shear action and therefore may not be as pronounced as with hollow or shell-type mediums, solid mediums such as disks, eight-side crystals, and irregularly-perimetered plates mass-balanced along the directions of vibration utilized may be used, as long as the medium is capable of sustaining therein a radial vibration pattern having a nodal region.

Thus, various hollow or solid mediums may be used in lieu of the specific bell members here disclosed, so long as radial vibrations imparted in relation to an axis generate a vibration pattern with substantially null regions as to such vibrations and rotation about the axis generates radial vibrations at such null regions through interaction with the imparted vibrations. Moreover, in the foregoing description, emphasis is placed on the most significant vibrations involved. The lip 14 in fact is believed to undergo complex vibrations in many modes, including radial, circumferential, and axial, all of which are coupled to some extent and may be detected. The practical operation and advantages of the apparatus, however, are believed to be essentially due to the described vibrations.

Also, the number of nodes and anti-nodes spaced about the perimeter of the high-Q medium may be increased from the four nodes and four anti-nodes obtained in the bell of the foregoing description to six or even eight by increasing the frequency of the flexing vibrations accordingly. This produces anti-nodal regions spaced from each other by l/n, where n is the number of anti-nodes in and nodal regions separated by substantially the same amount. The resulting vibration pattern will then have the anti-nodal regions separated from adjacent nodal regions by l80/2n. However, radial vibrations applied at an anti-nodal region of a pattern having a greater number of such regions would still be substantially independent of those applied at a nodal region and vice versa, such independence also being known mathematically as orthogonality. Thus, radial vibrations applied to either an anti-nodal region or a nodal region would still produce sub stantially no radial vibration at the other.

Nulling forcers in the foregoing description have been located within the confines of the bell and at a nodal region separate from those at which input-rotation-caused vibrations are detected. Since the latter vibrations are believed to be nulled by commensurate radial vibrations imparted at any to detect motion of a structure about an axis. Applications where the device may be used include those to indicate horizontal and vertical directions, to provide a strapped-down or gimballed reference platform, to stabilize a structure against external motions, or to navigate a vehicle over desired courses. Moreover, having described one embodiment of the present invention, it is understood that the specific terms and examples are employed in a descriptive sense and not for the purpose of limitation. It will be obvious to those skilled in the art that modification and changes may be made without departing from my invention and I, therefore, aim in the appended claims to cover such modifications and changes as fall within the true spirit and scope of my invention.

nodal region, the nulling forcers may be located adjacent to and operative on the inner or outer peripheries of the bell sides and also at the same nodal region as the sensor. Thus, as disclosed in the above cited Denis application, the nodal sensor and nulling forcer could both be mounted inside or outside the bell sides, or one could be located inside and the other outside, and they could be at the same or different nodal regions.

The subject invention has application wherever it is desired What I claim as new and desire to secure by letters of patent of the United States is:

1. An instrument to sense rotation of a platform about a predetermined axis, comprising in combination:

a. a platform;

b. a member carried by said platform and defining a perimeter about said axis and capable of high-Q radial vibrations, said member when radially exercised at a predetermined frequency sustaining therein a vibration pattern with substantially-null regions at first and second radii from said axis to said perimeter when vibrated along a third radius from said axis to the perimeter and generating at said null regions and along said first and second radii from said axis to the perimeter radial vibrations excited by the rotation of said member about said predetermined axis and by the effects of said radial exercise;

c. first forcer means carried by the platform and positioned to impart radial vibrations to said member on said perimeter along said third radius;

d. sensor means carried by the platform and responsive to vibrations at said first radius whereby with the platform at rest the sensor experiences substantially no response and with the platfrom rotating about said axis the sensor responds to radial vibrations along said first radius to indicate the presence of such axial rotation;

e. second forcer means carried by said platform and operative to impart at said second radius radial vibrations of frequency, sense, and magnitude balancing the vibrations to which the sensor responds; and

. means to measure the energy of the forcer required for balancing said null region vibrations, thereby indicating the rotation of the platform about the axis.

2. An instrument to sense rotation of a platform about a predetermined axis, comprising in combination:

a. a platform;

b. a high-Q member carried by said platform and defining a perimeter about said axis, said member capable of sustaining therein a vibration pattern defining a plurality of substantially-null regions when vibrated along a direction radial to said predetermined axis and angularly separated thereabout from said null regions and generating at said null regions radial vibrations excited thereat by the rotation of said member about said axis and the effects of said vibrations imparted along said radial direction;

c. first forcer means carried by said platform in close proximity to said perimeter and operatively connected to energizing means to impart said pattern of radial vibrations to said perimeter along said direction;

d. sensor means carried by the platform in close proximity to one of said null regions of said perimeter and operative to develop signals in response to radial vibrations at one of said null regions, whereby with the platform at rest the sensor develops substantially no response and with the platform rotating about said axis the sensor responds to said radial vibrations at one of said null regions and whereby said signals indicate such axial rotation; and

e. second forcer means carried bysaid platform in close proximity to said perimeter and operatively connected with said sensor to impart at one of said null regions radial vibrations of amplitude, phase, and frequency to diminish those sensed at said one of said null regions.

3. The apparatus of claim 2, wherein said radial direction is angularly disposed about said axis with respect to a said null region by an angle substantially l/2n and odd multiples thereof, where n is the number of null regions in produced in said pattern, whereby radial vibrations imparted along one of said direction and said null regions produce substantially no radial vibrations along the other of said radial direction and null regions.

4. The method of detecting movement of a high-Q member about a predetermined axis therethrough, said member being radially vibratable relative to said axis to produce a vibration pattern having regions vibratable relative to said axis in the presence of rotation and relatively quiescent otherwise, said method comprising the steps of:

a. imparting vibrations to said member along a first direction radial to said predetermined axis, thereby imparting to said member said vibration pattern with said relatively quiescent regions;

. sensing along a second direction radial to said axis and at a said quiescent region vibrations excited thereat by the interaction of movement of said member about said axis and the effects of said vibrations along said first direction;

and

c. imparting to said member at a said relatively quiescent region radial vibrations of magnitude, frequency, and phase corresponding to and substantially nulling said sensed vibrations, the energy required to diminish said sensed vibrations varying in accordance with the rotation of said member about said axis.

5. In an apparatus for detecting rotations of a platform about an input axis through the vibratory action of a bell-like member supported by the platform along the axis and having sides terminating in a lip vibrated in a pattern defining nodal and anti-nodal regions spaced alternately and equi-angularly circurnferentially thereabout:

a. sensor means supported by the platform in close proximity to said lip at one of said nodal regions and operatively connected with circuit means to sense radial vibrations produced at the nodal region due to the effect of the vibration pattern and rotation of the platform about the input axis; and

b. forcer means supported by the platform in close proximity to another of said nodal regions and operatively connected to said sensor means to apply vibrations in phase opposition to vibrations produced at said other region of magnitude and frequency to diminish said vibrations sensed by said sensor means.

6. In an apparatus for detecting motion of a platform about an axis:

a. a platform member including a base, a post upstanding therefrom along said axis and at least one opening formed in said post spaced radially from the axis;

b. a first electrode secured in said opening formed in said post and second and third electrodes secured to said platform;

c. a belllike conductive member having a center region supported by said platform along said axis and sides flaring outwards therefrom over said post and said first electrode, said sides capable of low-loss radial vibrations and defining a periphery adjacent said electrodes;

d. first circuit means operatively connected with one of said electrodes to develop a varying potential difference between said one electrode and said side to establish therein a vibration pattern defining nodal and anti-nodal regions spaced alternately and equi-angularly thereabout when the platform does not rotate;

e. second circuit means connected to another of said electrodes located at said nodal region, said second circuit,

operative to develop signals varying with the radial vibrations developed at said nodal region by the effects of said side vibrations and rotation of the platform about said axis; and

f. third circuit means operatively connected to a third of said electrodes located at,a nodal region and responsive to the signals developed by said second circuit means to develop a potential difference between said third electrode and said side, said potential difference establishing vibrations at said nodal regions diminishing those said vibrations developed in said sides by the effects of said vibration pattern and rotation of the platform about said axis.

7. The apparatus of claim 6, wherein a said nodal region is angularly disposed from a said anti-nodal region about said axis by an angle substantially 180/2n and odd multiples thereof, where n is the number of nodal regions produced in 180 of said vibration pattern, whereby radial vibrations imparted at one of said nodal and anti-nodal regions produce substantially no radial vibrations at the other of said regions.

8. An apparatus for detecting rotations of a platform about an axis comprised of:

a. a platform;

b. a high-Q member supported by said platform along said axis and defining an annular ring located thereabout, said ring capable of being vibrated radially in a pattern defining nodal and anti-nodal regions spaced alternately about the ring in the absence of platform rotation;

c. first forcer means carried by said platform in proximity to said ring at an anti-nodal region thereof and operatively connected with energizing means to impart radial vibrations in said ring defining said pattern;

d. sensor means carried by said platform in close proximity to said ring at a first nodalregion thereof and operatively connected with circuit means to develop signals varying with the magnitude of radial ring; vibrations at said first nodal region in the presence of platform rotation about said axis; and

e. second forcer means supported by said platform in close proximity to a second said nodal region and operatively connected in circuit with said sensor to impart radial vibrations to said second nodal region in phase opposition and magnitude to the radial vibrations produced thereat with rotation of the platform about said axis, whereby the vibrations sensed at said first nodal region are diminished.

9. The apparatus of claim 8 wherein a said nodal region is angularly disposed from a said anti-nodal region about said axis by an angle substantially /2n degrees, where n is the number of said null regions in 180, whereby radial vibrations imparted at one of said nodal and anti-nodal regions produce substantially no radial vibrations at the other of said nodal and anti-nodal regions.

10. The apparatus of claim 8 wherein the frequency of vibrations imparted by said first forcer are such as to generate standing waves extending circumferentially about said lip and defining said radial vibration pattern and wherein one of said first forcer, second forcer, and sensor is carried by said platform within the confines of said annular ring.

275 UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No. 3 656,354 Dated April 18, 1972 In ent David D. Lvnch It is certified that error appears in the above-identified patent and that said Letters Patent are hereby corrected as shown below:

in the references, "Newton" should read Newton, Jr. -17

Column 10, Line 3, "dc-Dc" should read dc-dc Line 11, "16 should read T6 Column 13, Line 31, "%32" should read T32 Line 33, "T32" should read connected Y Line .1 I 1 45, "relon" should read reglon umn Column 17, in the TABLE OF FIGURE. 3 COMPONENTS AND VALUES,

Line 28, Column Value (ohms) 10 K to be inserted; Line 30, delete "K" Signed and sealed this 6th day of March 1973.

(SEAL) Attest:

EDWARD M.FLETCHER,JR. I ROBERT GOTTSCHALK Attesting Officer Commissioner of Patents 

1. An instrument to sense rotation of a platform about a predetermined axis, comprising in combination: a. a platform; b. a member carried by said platform and defining a perimeter about said axis and capable of high-Q radial vibrations, said member when radially exercised at a predetermined frequency sustaining therein a vibration pattern with substantially-null regions at first and second radii from said axis to said perimeter when vibrated along a third radius from said axis to the perimeter and generating at said null regions and along said first and second radii from said axis to the perimeter radial vibrations excited by the rotation of said member about said predetermined axis and by the effects of said radial exercise; c. first forcer means carried by the platform and positioned to impaRt radial vibrations to said member on said perimeter along said third radius; d. sensor means carried by the platform and responsive to vibrations at said first radius whereby with the platform at rest the sensor experiences substantially no response and with the platfrom rotating about said axis the sensor responds to radial vibrations along said first radius to indicate the presence of such axial rotation; e. second forcer means carried by said platform and operative to impart at said second radius radial vibrations of frequency, sense, and magnitude balancing the vibrations to which the sensor responds; and f. means to measure the energy of the forcer required for balancing said null region vibrations, thereby indicating the rotation of the platform about the axis.
 2. An instrument to sense rotation of a platform about a predetermined axis, comprising in combination: a. a platform; b. a high-Q member carried by said platform and defining a perimeter about said axis, said member capable of sustaining therein a vibration pattern defining a plurality of substantially-null regions when vibrated along a direction radial to said predetermined axis and angularly separated thereabout from said null regions and generating at said null regions radial vibrations excited thereat by the rotation of said member about said axis and the effects of said vibrations imparted along said radial direction; c. first forcer means carried by said platform in close proximity to said perimeter and operatively connected to energizing means to impart said pattern of radial vibrations to said perimeter along said direction; d. sensor means carried by the platform in close proximity to one of said null regions of said perimeter and operative to develop signals in response to radial vibrations at one of said null regions, whereby with the platform at rest the sensor develops substantially no response and with the platform rotating about said axis the sensor responds to said radial vibrations at one of said null regions and whereby said signals indicate such axial rotation; and e. second forcer means carried by said platform in close proximity to said perimeter and operatively connected with said sensor to impart at one of said null regions radial vibrations of amplitude, phase, and frequency to diminish those sensed at said one of said null regions.
 3. The apparatus of claim 2, wherein said radial direction is angularly disposed about said axis with respect to a said null region by an angle substantially 180*/2n and odd multiples thereof, where n is the number of null regions in 180* produced in said pattern, whereby radial vibrations imparted along one of said direction and said null regions produce substantially no radial vibrations along the other of said radial direction and null regions.
 4. The method of detecting movement of a high-Q member about a predetermined axis therethrough, said member being radially vibratable relative to said axis to produce a vibration pattern having regions vibratable relative to said axis in the presence of rotation and relatively quiescent otherwise, said method comprising the steps of: a. imparting vibrations to said member along a first direction radial to said predetermined axis, thereby imparting to said member said vibration pattern with said relatively quiescent regions; b. sensing along a second direction radial to said axis and at a said quiescent region vibrations excited thereat by the interaction of movement of said member about said axis and the effects of said vibrations along said first direction; and c. imparting to said member at a said relatively quiescent region radial vibrations of magnitude, frequency, and phase corresponding to and substantially nulling said sensed vibrations, the energy required to diminish said sensed vibrations varying in accordance with the rotation of said member about said axis.
 5. In an apparatus for detecting rotations of a platform about an input axis through the vibratory action of a bell-like member supported by the platform along the axis and having sides terminating in a lip vibrated in a pattern defining nodal and anti-nodal regions spaced alternately and equi-angularly circumferentially thereabout: a. sensor means supported by the platform in close proximity to said lip at one of said nodal regions and operatively connected with circuit means to sense radial vibrations produced at the nodal region due to the effect of the vibration pattern and rotation of the platform about the input axis; and b. forcer means supported by the platform in close proximity to another of said nodal regions and operatively connected to said sensor means to apply vibrations in phase opposition to vibrations produced at said other region of magnitude and frequency to diminish said vibrations sensed by said sensor means.
 6. In an apparatus for detecting motion of a platform about an axis: a. a platform member including a base, a post upstanding therefrom along said axis and at least one opening formed in said post spaced radially from the axis; b. a first electrode secured in said opening formed in said post and second and third electrodes secured to said platform; c. a bell-like conductive member having a center region supported by said platform along said axis and sides flaring outwards therefrom over said post and said first electrode, said sides capable of low-loss radial vibrations and defining a periphery adjacent said electrodes; d. first circuit means operatively connected with one of said electrodes to develop a varying potential difference between said one electrode and said side to establish therein a vibration pattern defining nodal and anti-nodal regions spaced alternately and equi-angularly thereabout when the platform does not rotate; e. second circuit means connected to another of said electrodes located at said nodal region, said second circuit operative to develop signals varying with the radial vibrations developed at said nodal region by the effects of said side vibrations and rotation of the platform about said axis; and f. third circuit means operatively connected to a third of said electrodes located at a nodal region and responsive to the signals developed by said second circuit means to develop a potential difference between said third electrode and said side, said potential difference establishing vibrations at said nodal regions diminishing those said vibrations developed in said sides by the effects of said vibration pattern and rotation of the platform about said axis.
 7. The apparatus of claim 6, wherein a said nodal region is angularly disposed from a said anti-nodal region about said axis by an angle substantially 180*/2n and odd multiples thereof, where n is the number of nodal regions produced in 180* of said vibration pattern, whereby radial vibrations imparted at one of said nodal and anti-nodal regions produce substantially no radial vibrations at the other of said regions.
 8. An apparatus for detecting rotations of a platform about an axis comprised of: a. a platform; b. a high-Q member supported by said platform along said axis and defining an annular ring located thereabout, said ring capable of being vibrated radially in a pattern defining nodal and anti-nodal regions spaced alternately about the ring in the absence of platform rotation; c. first forcer means carried by said platform in proximity to said ring at an anti-nodal region thereof and operatively connected with energizing means to impart radial vibrations in said ring defining said pattern; d. sensor means carried by said platform in close proximity to said ring at a first nodal region thereof and operatively connected with circuit means to develop signals varying with the magnitude of radial ring vibrations at said first nodal region in the presence of platform rotation about said axis; anD e. second forcer means supported by said platform in close proximity to a second said nodal region and operatively connected in circuit with said sensor to impart radial vibrations to said second nodal region in phase opposition and magnitude to the radial vibrations produced thereat with rotation of the platform about said axis, whereby the vibrations sensed at said first nodal region are diminished.
 9. The apparatus of claim 8 wherein a said nodal region is angularly disposed from a said anti-nodal region about said axis by an angle substantially 180*/2n degrees, where n is the number of said null regions in 180*, whereby radial vibrations imparted at one of said nodal and anti-nodal regions produce substantially no radial vibrations at the other of said nodal and anti-nodal regions.
 10. The apparatus of claim 8 wherein the frequency of vibrations imparted by said first forcer are such as to generate standing waves extending circumferentially about said lip and defining said radial vibration pattern and wherein one of said first forcer, second forcer, and sensor is carried by said platform within the confines of said annular ring. 